Project 3: Numeric Representation Deep Dive

A comprehensive numeric representation toolkit that explores integer representations, floating-point IEEE 754, safe conversions, and numeric edge cases.

Quick Reference

Attribute Value
Primary Language C
Alternative Languages Python (for verification)
Difficulty Level 3 - Advanced
Time Estimate See main guide
Knowledge Area Computer Architecture, Numeric Computation
Tooling GCC, GDB, bc (calculator)
Prerequisites See main guide

What You Will Build

A comprehensive numeric representation toolkit that explores integer representations, floating-point IEEE 754, safe conversions, and numeric edge cases.

Why It Matters

This project builds core skills that appear repeatedly in real-world systems and tooling.

Core Challenges

  • Visualizing binary representations → Maps to understanding bit patterns
  • IEEE 754 decomposition → Maps to understanding floating-point precision
  • Safe conversion library → Maps to avoiding overflow vulnerabilities

Key Concepts

  • Map the project to core concepts before you code.

Real-World Outcome

# 1. Integer representation
$ ./numeric_tools int 127
Decimal:  127
Binary:   01111111
Hex:      0x7F
Bits:     8
Signed:   yes
Two's complement representation

$ ./numeric_tools int -1
Decimal:  -1
Binary:   11111111111111111111111111111111
Hex:      0xFFFFFFFF
Bits:     32
Note: All 1s is two's complement representation of -1

# 2. IEEE 754 floating-point
$ ./numeric_tools float 3.14159
Value:     3.14159
Bits:      01000000010010010000111111010000
Sign:      0 (positive)
Exponent:  10000000 (biased: 128, actual: 1)
Mantissa:  10010010000111111010000
Formula:   (-1)^0 × 1.57079637... × 2^1 = 3.14159...

$ ./numeric_tools float 0.1
Value:     0.1
WARNING:   0.1 cannot be exactly represented in binary floating-point!
Actual:    0.100000001490116119384765625
Error:     1.49e-09

# 3. Safe arithmetic
$ ./numeric_tools safe_add 2147483647 1
INT_MAX + 1 would overflow!
Safe result: OVERFLOW_ERROR

$ ./numeric_tools safe_multiply 65536 65536
65536 * 65536 would overflow 32-bit int!
Use int64_t for result: 4294967296

# 4. Conversion safety
$ ./numeric_tools convert -5 unsigned
Converting -5 to unsigned...
WARNING: Converting negative to unsigned!
Result: 4294967291 (wraps around as per C standard)
This IS defined behavior but probably not what you want.

Implementation Guide

  1. Reproduce the simplest happy-path scenario.
  2. Build the smallest working version of the core feature.
  3. Add input validation and error handling.
  4. Add instrumentation/logging to confirm behavior.
  5. Refactor into clean modules with tests.

Milestones

  • Milestone 1: Minimal working program that runs end-to-end.
  • Milestone 2: Correct outputs for typical inputs.
  • Milestone 3: Robust handling of edge cases.
  • Milestone 4: Clean structure and documented usage.

Validation Checklist

  • Output matches the real-world outcome example
  • Handles invalid inputs safely
  • Provides clear errors and exit codes
  • Repeatable results across runs

References

  • Main guide: PROFESSIONAL_C_PROGRAMMING_MASTERY.md
  • Effective C, 2nd Edition by Robert C. Seacord